Number busting

We can also investigate numbers using things like a 10 frame. Which is just a structure that we use to help us understand a numbers relationship to other numbers and the numbers that sit inside of it.

And I started to draw a 10 frame here but I thought it might be good to show you what it looks like.

You might also have a book at home about helping a child with literacy and numeracy that has a 10 frame in the middle.

But it's just a really big rectangle. So I've already drawn the first line and in this case today I'm gonna draw mine like it's standing on its' skinny edge so that it's vertical. And I draw my rectangle and then I need to partition it in half, this way and now, I know because I've played around with them a lot, I need to do some internal lines so that I end up with five boxes on one side and five on the other. And so I know that means I need four lines so I'm gonna put them about here. One, two, three, four and I should have five boxes on this side. One, two, three, four, five and five on this side, one, two, three, four, five, which means I should have ten all together.

One, two, three, four, five, six, seven, eight, nine, ten. Which is why it's called a ten frame.

So what I thought we could play around with is seven and explore different ways of thinking about seven today.

So seven is, and I could represent it like this, and what I see here is seven is one column of five and two more.

So seven is five and two.

Do you have another way Ayesh that you could arrange it?

Sure, so I'm going to have a look at seven as four and three.

Okay so seven is four and opps, and three.

And oh you know what else I'm seeing, if I move this one Ayesh that helps me. I can also see that there's three blank spaces, so 7 is 3 less than 10. Cause it's a 10 frame.

Do you think there's another way we could see 7?

So if I move this one over here I can see 6 and one more which makes 7.

Do you know what we could do? Because mathematicians sometimes use color Ayesh, so if I moved this, swapped this one here for a blue one. Does that help you see your six and one?

It does, yeah it does make it clearer.

So we could even record it like that too, so we could say 6 and 1. So we can see that the different colors are corresponding to our pretend counters. Okay, okay now that we're doing this, I could do something else. I'm going to use these two and say in this case what I'm seeing. I can still see your six and your one but the six is actually a 4 and a 2 so I could say 7 is 4 and 2 and 1. 7 is 4 and 2... and one more.

Oh I can see something else that I'd like to share. So in this four I can see two and two. So if I swap those out I can see two and two more and another two more is six and one more makes seven. So seven is 2 and 2 and... 2... and... 1 more. Does that represent your thinking Ayesh?

It does, I can see how the colors are shown by our pretend counters.

And you know what else we could do for this one, is we could actually say that this is three twos and one more. Because look, there's one two, a second two and three 2's. One two, a second two, three 2s and one more! There's a lot of things about 7! I wonder if you can find any extras?

So we were thinking about number busting and we thought we could probably do some number busting with Lego or investigate part, part, whole number knowledge onto Lego.

And so I've got a board here, my Lego board and I've got an 8 brick and what we were wondering is can we use the Lego then to show us different ways of thinking about or renaming 8.

Oh, good idea.

So Barbara, have you got some bricks that you could use that would fit into there?

So, and I could record it for us.

Ok.

So I can say 8 is....

Well ,I know that 8 is also 4 and 4.

Ok. 4 and 4. Ayesh, have you got any?

I've got some Lego here that can make 8. So it's 2 and 2 which is 4. And 2 more, which is 6 and 2 more which makes 8. So 2 and 2 and 2 and 2.

And if I wanted to I could look at it and say we've got one, two, three, four twos, so I could also describe that as 4 twos.

And mathematicians would call that multiplicative.

Can I have a go?

Yes.

Umm ok, what about this? What about a 4 and a 2 and a 1 and a 1. Or I should read it across this way. A 1 and a 1 and a 2 and a 4. 1 and 1 and 2 and 4. Do you have another way Barbara?

I do. So this one actually uses a 3, which we haven't used yet. 3 and 2 and 2 and then 1 more.

[Silent placing of bricks for three rows.]

So, I've got a 2 and a 6.

And then I think, yep, that's different, a three, a four and one more.

I wonder, are there any others?